Problem: Solve for $x$ and $y$ using elimination. ${-4x-4y = -48}$ ${-5x+3y = -28}$
We can eliminate $y$ by adding the equations together when the $y$ coefficients have opposite signs. Multiply the top equation by $3$ and the bottom equation by $4$ ${-12x-12y = -144}$ $-20x+12y = -112$ Add the top and bottom equations together. $-32x = -256$ $\dfrac{-32x}{{-32}} = \dfrac{-256}{{-32}}$ ${x = 8}$ Now that you know ${x = 8}$ , plug it back into $\thinspace {-4x-4y = -48}\thinspace$ to find $y$ ${-4}{(8)}{ - 4y = -48}$ $-32-4y = -48$ $-32{+32} - 4y = -48{+32}$ $-4y = -16$ $\dfrac{-4y}{{-4}} = \dfrac{-16}{{-4}}$ ${y = 4}$ You can also plug ${x = 8}$ into $\thinspace {-5x+3y = -28}\thinspace$ and get the same answer for $y$ : ${-5}{(8)}{ + 3y = -28}$ ${y = 4}$